Nuprl Lemma : empty-fset-closed
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[fs:(T ⟶ T) List]. ({} closed under fs)
Proof
Definitions occuring in Statement :
fset-closed: (s closed under fs),
empty-fset: {},
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fset-closed: (s closed under fs),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
l_all: (∀x∈L.P[x])
Lemmas referenced :
mem_empty_lemma,
l_all_iff,
all_wf,
isect_wf,
false_wf,
l_member_wf,
int_seg_wf,
length_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
isectElimination,
functionEquality,
hypothesisEquality,
lambdaEquality,
setEquality,
productElimination,
independent_functionElimination,
lambdaFormation,
because_Cache,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[fs:(T {}\mrightarrow{} T) List]. (\{\} closed under fs)
Date html generated:
2016_05_14-PM-03_44_45
Last ObjectModification:
2015_12_26-PM-06_38_09
Theory : finite!sets
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